Book embedding: vertices on a line (spine), edges assigned to pages (half-planes). No two edges on same page may cross. Book thickness bt(G) = minimum pages. Planar ≤ 4 (Yannakakis 1989). Outerplanar = 1. Trees = 1. Stack layout interpretation.
How to Use
Select graph:
- Pages: Assign edges
- Spine: Vertex order
- bt: Book thickness
Planar Graphs
Every planar graph has bt ≤ 4 (Yannakakis 1989, improved from 9). Tight: some planar graphs need 4 pages. Outerplanar: 1 page suffices. Hamiltonian planar: 2 pages suffice (Bernhart-Kainen 1979).
Stack Layout
Book embedding = stack layout: spine order = processing order, pages = stacks. Edge (u,v) on page = push u, pop at v. No crossing = proper nesting (LIFO). Dual to queue layouts (FIFO). Fundamental in CS.
Step-by-Step Instructions
- 1Select graph.
- 2Order spine.
- 3Assign edges to pages.
- 4Check crossings.
- 5Minimize pages.